# Classical zero-knowledge arguments for quantum computations

## TL;DR

This paper presents a classical-verifier, quantum-prover zero-knowledge argument system for all languages in QMA, combining recent advances to achieve soundness against quantum provers and zero-knowledge properties.

## Contribution

It introduces a new zero-knowledge argument system for QMA that uses a classical verifier and quantum prover, building on recent foundational results.

## Key findings

- Achieves zero-knowledge for classical and quantum verifiers.
- Ensures soundness against quantum polynomial-time provers.
- Builds on recent zero-knowledge and argument systems for QMA.

## Abstract

We show that every language in QMA admits a classical-verifier, quantum-prover zero-knowledge argument system which is sound against quantum polynomial-time provers and zero-knowledge for classical (and quantum) polynomial-time verifiers. The protocol builds upon two recent results: a computational zero-knowledge proof system for languages in QMA, with a quantum verifier, introduced by Broadbent et al. (FOCS 2016), and an argument system for languages in QMA, with a classical verifier, introduced by Mahadev (FOCS 2018).